@che
i am also getting the same answer.
The equation of circle(s) of radius 1 & touching the circles x2 + y2 - 2|x| = 0 is ?
the given equation is same as
x2 + y2 - 2|x| +1=1
w;hich is same as (|x|-1)2+y2=1
Which are 2 circles of radius one and your answers are correct :)